Problem: What do the following two equations represent? $x-y = -3$ $x-y = 5$
Answer: Putting the first equation in $y = mx + b$ form gives: $x-y = -3$ $-y = -x-3$ $y = 1x + 3$ Putting the second equation in $y = mx + b$ form gives: $x-y = 5$ $-y = -x+5$ $y = 1x - 5$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.